TY - GEN
T1 - Interaction Improves Two-party Nonparametric Pointwise Density Estimation
AU - Liu, Jingbo
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - We characterize the minimax rates in two-party nonparametric pointwise density estimation in terms of the communication costs, under either the one-way or interactive protocols. It is shown that allowing interactive communications can strictly improve the minimax rate, a phenomenon not seen the parametric counterpart of the problem (assuming that the parameters are fixed). Moreover, a few rounds of interactions achieve the interactive minimax rate: the number of rounds can grow as slowly as the super-logarithm (i.e., inverse tetration) of k. The proof of the upper bound is based on a novel multi-round scheme for estimating the joint distribution of a pair of biased Bernoulli variables.
AB - We characterize the minimax rates in two-party nonparametric pointwise density estimation in terms of the communication costs, under either the one-way or interactive protocols. It is shown that allowing interactive communications can strictly improve the minimax rate, a phenomenon not seen the parametric counterpart of the problem (assuming that the parameters are fixed). Moreover, a few rounds of interactions achieve the interactive minimax rate: the number of rounds can grow as slowly as the super-logarithm (i.e., inverse tetration) of k. The proof of the upper bound is based on a novel multi-round scheme for estimating the joint distribution of a pair of biased Bernoulli variables.
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U2 - 10.1109/ISIT50566.2022.9834454
DO - 10.1109/ISIT50566.2022.9834454
M3 - Conference contribution
AN - SCOPUS:85136256180
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 904
EP - 909
BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022
Y2 - 26 June 2022 through 1 July 2022
ER -